### Fermi surfaces

Fermi surfaces can be studied in the gauge string duality by calculating the propagation of bulk fermions in the presence of a charged black hole. The signature of a holographic Fermi surface is that the bulk fermion has a normal mode with a momentum $k_F$ which is some finite multiple of the chemical potential $\mu$ of the black hole.

"Fermi surfaces in N=4 Super-Yang-Mills theory" by O. DeWolfe, S. Gubser, and C. Rosen provides explicit embeddings of holographic Fermi surface constructions into type IIB string theory on $AdS_5 \times S^5$, whose field theory dual (N=4 super-Yang-Mills theory) is the best understood of all strongly coupled four-dimensional conformal field theories. The figure shows the value of the Fermi momentum as a function of the ratio $\mu_R$ of two of the independent chemical potentials in N=4 SYM. An interesting feature of the Green's function emerges in the limit $\mu_R \to 0$: one obtains a marginal Fermi liquid, in which dissipative effects are only logarithmically enhanced over reactive effects.